Abstract

Stochastic reconstruction techniques are developed for mapping the
interior optical properties of tissues from exterior frequency-domain
photon migration measurements at the air–tissue
interface. Parameter fields of absorption cross section,
fluorescence lifetime, and quantum efficiency are accurately
reconstructed from simulated noisy measurements of phase shift and
amplitude modulation by use of a recursive, Bayesian, minimum-variance
estimator known as the approximate extended Kalman
filter. Parameter field updates are followed by data-driven
zonation to improve the accuracy, stability, and computational
efficiency of the method by moving the system from an underdetermined
toward an overdetermined set of equations. These methods were
originally developed by Eppstein and Dougherty [Water Resources Res. 32, 3321 (1996)] for applications in
geohydrology. Estimates are constrained to within feasible ranges
by modeling of parameters as β-distributed random variables. No
arbitrary smoothing, regularization, or interpolation is
required. Results are compared with those determined by use of
Newton–Raphson-based inversions. The speed and accuracy of these
preliminary Bayesian reconstructions suggest the near-future
application of this inversion technology to three-dimensional
biomedical imaging with frequency-domain photon migration.

References

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